 Hi and welcome to the session. I am Asha and I am going to help you with the following problem that says find the value of tan 15 degree. Let us now begin with the solution and we have to find the value of tan 15 degree which can be written as tan 60 degree minus 45 degree. Now formula of tan A minus B is equal to tan A minus tan B upon 1 plus tan A into tan B and I am comparing this with tan 60 degree minus 40 degree. We find there that A is 60 degree and B is 45 degree. So, it can further be written as tan 60 degree minus tan 45 degree upon 1 plus tan 60 degree into tan 45 degree which is further equal to tan 60 degree is root over 3 minus tan 45 degree is 1 upon 1 plus root over 3 into 1 which is equal to root over 3 minus 1 upon 1 plus root over 3. Now let us rationalize it. So, multiplying the numerator and denominator by 1 minus root 3 which is the conjugate of 1 plus root 3 we can further write it as root 3 minus 1 into 1 minus root 3 upon 1 square minus root 3 square since A minus B into A plus B is equal to A square minus B square and here in place of A we have 1 and in place of B we have root 3. So, the denominator we have 1 minus 3 and in the numerator we can write it as minus of root 3 minus 1 whole square minus 1 common from this bracket. Now it can further be written as minus of root 3 square minus 2 root 3 plus 1 upon minus 2 since this is in the form of A minus B whole square whose formula is A square minus 2 AB plus B square. This is further equal to minus 3 minus 2 root 3 plus 1 upon minus 2. Now this minus sign cancels out with this minus sign and we have 4 minus 2 root 3 upon 2. Now taking 2 common from the numerator we have 2 minus root 3 upon 2. Now this 2 cancels out with 2 and we have 2 minus root 3. Hence, the value of tan 15 degree is equal to 2 minus root 3. So, this completes the solution. Hope you enjoyed it. Take care and have a good day.